Pyramid #280
Generating function
$$U_{280}(x, y) = \frac{- y - \sqrt{- 4 x^{2} + y^{2} - 2 y + 1} + 1}{2 x^{2}}$$
Explicit formula
$$T_{280}(n, m, k) = \frac{k \left(\left(-1\right)^{n} + 1\right) {\binom{k + n}{\frac{n}{2}}} {\binom{k + m + n - 1}{m}}}{2 k + 2 n}$$
Data table
1 1 1 1 1 1 1
0 0 0 0 0 0 0
1 3 6 1 15 21 28
0 0 0 0 0 0 0
2 1 3 7 14 252 42
0 0 0 0 0 0 0
5 35 14 42 105 231 462
Export
expand_less